The two sets of governing equations for MFMS and TF models presented in Eqs. REF , REF , REF , REF , and REF  have been implemented in a code named Ebysus  [1]}, which is an extension of the single-fluid radiative MHD code Bifrost  [2]}. Note that the governing equations can be rewritten in a more compact form which allows us to distinguish the nature of the different terms involved, as shown in Appendix .
